The information theory (mathematical) definition of randomness is explained nicely in Chapter V of An Introduction to Information Theory: http://www.amazon.com

The information theory (mathematical) definition of randomness is explained nicely in Chapter V of An Introduction to Information Theory: http://www.amazon.com/Introduction-Information-Theory-Symbols-Mathematics/dp/0486240614/ http://www.amazon.com/Introduction-Information-Theory-Symbol... In the particular case of a series of n equally-probably, independent events, the entropy is given as H = - log 1/n, measured in bits. For example, the entropy of a fair die is - log 1/6 = 2.58 bits per throw. In this case, the random event is words chosen from a word list. Four words are chosen from fifty thousand, with each word having equal probability of being chosen. So the entropy (measure of randomness) is - log 1/50,000 = 15.6 bits per word, or 62.4 bits per four-word combination. (The script also adds random numbers or symbols, to add up to 90 bits.)